Spatial Error Terms Research Articles

Using a spatial autoregressive model with spatial autoregressive disturbances to investigate origin-destination trip flows.

Spatial interaction models with spatial origin-destination (OD) filters are powerful tools to characterize trip flows in space, which is a classic and important problem in regional science. To the authors' knowledge, existing studies adopting OD filters mostly specify the spatial dependence as an autoregressive process, which may not be the full picture of spatial effects. To examine the problem, this paper proposes the hypotheses that 1) spatial OD dependences can take place in both the spatial autoregressive term and the spatial error term in a spatial interaction model. 2) Estimating a spatial autoregressive model with spatial autoregressive disturbances (SARAR) model with OD filters would disentangle where the spatial dependence exists and by how much. 3) The marginal effects obtained from SARAR models would be preferred to analysts when SARAR models outperform spatial autoregressive (SAR) models and spatial error models (SEM) from the statistical point of view. To assess these hypotheses, this paper specifies, estimates, and applies SARAR models with OD filters to investigate trip distributions. By comparing against alternative models, this paper investigates the estimation results in SAR, SEM and SARAR models using an empirical data collected from Hangzhou, China. The contribution of this paper is to be the first in developing an SARAR model with OD filters for trip distribution analyses and examining its performance.

Human Capital and Regional Economic Growth in Indonesia: A Spatial Analysis Approach

Endogenous growth theory assumes that human capital is a prominent factor in regional economic growth. However, the imbalance of human capital between regions is still a major problem in economic growth in Indonesia. Previous studies on regional economic growth have recognized the importance of considering spatial aspects as a determinant of regional economic growth. The geographical area in the form of an archipelago with a large number of administrative districts and cities produces pros and cons regarding the influence of spatial aspects on the regional growth of urban districts. This study aims to analyze the distribution of human capital using the Alternative Human Development Index (AHDI) approach and the effect of human capital and spatial aspects on the regional economic growth of urban districts in Indonesia within the framework of endogenous growth theory. The research method uses geometric mean to measure the Alternative Human Development Index, Geographic Information System (GIS) to see the distribution of human capital and regional economic growth in Indonesia, and the spatial regression Spatial Autoregressive Moving Average (SARMA) used to analyze the spatial aspects of human capital and regional economic growth in Indonesia. The results show that human capital in Indonesia is still unequal between the western and eastern parts of Indonesia. Human capital and spatial factors have positive effects and are the most influential determinants of Indonesia's regional economic growth, as indicated by the value of the spatial lag weight matrix of the dependent variable (ρ) and the spatial error term (λ) that is positive.

Spatial dependence and competition between U.S. airports

U.S. commercial airports are public infrastructure owned and operated by government authorities. If so, do public commercial airports compete with each other? In this study, we investigated airport competition by applying the data of 59 U.S. hub airports from 2009 to 2019 in a Cliff-Ord typed spatial model. The model includes two modules: the first module captures the impact of neighboring airports on the airport's output with a spatial lag dependent variable, while the second module considers the bias resulting from spatial autoregressive error term. The results suggest that the airports' outputs are spatially and negatively dependent; namely, an increase in the outputs of neighboring airports leads to a decrease in the output of an airport. This indicates the existence of airport competition. In addition, we found that the outputs of airports governed by city and state are greater than those of ones governed by the port/airport authority after controlling for all other factors.

Statistical modeling and monitoring of image data in the presence of temporal and spatial correlations

In this paper, the regression-based approach was developed to monitor image data under two-scale analysis. In the first scale, wavelet transformation was used to extract the main features of geometric profile created from the images. The next scale was to monitor the small-scale components which could be expressed by correlation in error terms. To monitor correlation in error terms, one parametric and one non-parametric methods were developed. Parameters of the parametric model including spatial correlation coefficient and error term variance were estimated using Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators, respectively. In non-parametric method, no assumption was made about the structure of correlation in error terms. To extract useful information about the nature of correlation in error terms, Functional Principal Component Analysis (FPCA) was used. After extracting features for both scales, some appropriate test statistics were computed. Then, monitoring the process was performed by plotting these test statistics on corresponding control charts. Simulation and industrial case studies were also performed to evaluate the proposed method’s performance in detecting different shifts. The results indicated the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identify the source of variability.

Estimating the effect of friction on crash risk: Reducing the effect of omitted variable bias that results from spatial correlation

Omitted variable bias is one of the main factors that lead to incorrect estimates of the effect of a variable on the expected number of crashes using regression modeling. We propose to use differencing of the (spatially adjacent) variables to reduce the effect of omitted variable bias. Differencing is a linear transformation that preserves the structure of the (generalized) linear model but can often result in significantly reducing the correlation between the variables. It is special case of (generalized) partial linear model regression which itself is a special case of a generalized additive model (GAM). In the spatial context used in this paper, differencing is similar to the well-known approach of including a spatial correlation structure (spatial error term) in the analysis of crash data. It is generally not clear how to interpret the results of models that include a spatial correlation structure and whether and how the added spatial correlation structure reduces the bias in the estimated regression parameters. However, for the case of differencing, it becomes clear how the effect of omitted variable bias is reduced by reducing the correlation between the variable of interest and the omitted variables. The order of differencing determines the dominant spatial scales of the variables considered in the model which affect how much the correlation is reduced. This reveals that omitted variable bias can be reduced when there are spatial scales at which the covariate of interest varies but the omitted variables either 1) are relatively homogeneous or 2) have variations that are not correlated to those of the variable of interest.

Spatial-nonparametric regression: an approach for monitoring image data

Statistical process control plays a significant role in manufacturing industries as processes become more advanced and manufactured products more complex. Because of the increasing sensitivity of the processes and the inadequacy of the methods based on human inspection, use of product images in statistical process control has been considered by some researchers. In this paper, a regression-based method is developed to monitor image data under two-scale analysis. In the first scale, wavelet transformation is used to extract the main features of geometric profile created from the images. The next scale is to monitor the small-scale components which could be expressed by correlation in error terms. To monitor correlation in error terms, a parametric method is developed. Parameters of the parametric model including spatial correlation coefficient and error term variance are estimated using Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators, respectively. After extracting features for both scales, some appropriate test statistics are computed. Then, monitoring the process is performed by plotting these test statistics on corresponding control charts. Performance of the proposed method is evaluated in terms of run length measures and the difference between the actual value and the estimated value of change-points. Simulation studies are performed on tile images, and the results show the capability of the proposed method in detecting out-of-control conditions and estimating the change-point. The results also indicate the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identifying the source of variability.

Regionally Divergent Patterns in Factors Affecting Municipal Waste Production: The Polish Perspective

This article attempts to identify factors impacting on the quantity of municipal waste in Polish 2478 communes (LAU-2), taking into account the variability of particular determinants’ influence depending on their regional diversification. The analysis covers the years 2005–2018. The dependent variable is the volume of municipal waste in kg per capita, whereas the group of determinants include: economic and human development, uncontrolled dumping sites, population density, population at the working age, migration, tourism, urbanization, dwellings and housing, retail sales, entities, education, and investments in waste management. The geographically weighted regression with spatial error term (GWR–SEM) was employed in this study. The model enabled not only the specification of the waste production determinants, but also the analysis of the variability in the strength and direction of dependencies occurring between the examined variables in individual communes. The results proved that the higher the level of education, the less waste is generated (in north-central Poland); the business entities and working-age population are crucial for the waste quantity in communes of eastern Poland; the factors most important to regional range affecting the waste quantity are urban and business development, and most important to strength are higher education and the share of working-age individuals.

Spatial variation in the frequency of knockdown resistance genotypes in Florida Aedes aegypti populations

BackgroundThe development of insecticide resistance in disease-vectoring mosquito species can lead to vector control failure and disease resurgence. However, insecticide applications remain an essential public health intervention. In Florida, insecticide resistance in Aedes aegypti, an anthropophilic mosquito species capable of transmitting dengue, chikungunya, and Zika virus, is a major concern. Understanding the location, scale, and driving factors of insecticide resistance can enhance the ability of vector control organizations to target populations effectively.MethodsWe used previously collected data on frequencies of mutations that confer resistance to commonly used pyrethroid insecticides in Ae. aegypti specimens from 62 sites distributed across 18 counties in Florida. To determine the scale of clustering for the most resistant variant, we used a Ripley’s K function. We also used a spatial scanning statistic technique to identify locations of clusters where higher than expected frequencies of susceptible or resistant mosquitoes occurred. We then tested for associations between landscape, demographic, and insecticide-use factors using a beta regression modelling approach and evaluated the effect of spatial lag and spatial error terms on overall explanatory power of these models.ResultsThe scale at which maximum clustering of the most resistant variant occurs is approximately 20 kilometers. We identified statistically significant clusters of genotypes associated with resistance in several coastal cities, although some of these clusters were near significant clusters of susceptible mosquitoes, indicating selection pressures vary at the local scale. Vegetation density, distance from roads, and pyrethroid-use by vector control districts were consistently significant predictors of knockdown resistance genotype frequency in the top-performing beta regression models, although pyrethroid use surprisingly had a negatively associated with resistance. The incorporation of spatial lags resulted in improvements to the fit and explanatory power of the models, indicating an underlying diffusion process likely explains some of the spatial patterns observed.ConclusionsThe genetic mutations that confer resistance to pyrethroids in Ae. aegypti mosquitoes in Florida exhibit spatial autocorrelation and patterns that can be partially explained by landscape and insecticide-use factors. Further work at local scales should be able to identify the mechanisms by which these variables influence selection for alleles associated with resistance.

Florida neighborhood analysis of social determinants and their relationship to life expectancy

BackgroundSocial determinants of health (SDOH) contribute to unequal life expectancy (LE). Only a handful of papers have analyzed these relationships at the neighborhood level as opposed to the county level. This study draws on both the SDOH and social vulnerability literature to identify relevant factors affecting LE.MethodsLE was calculated from mortality records for Florida from 2009 to 2013 for 3640 census tracts with reliable estimates. A spatial Durbin error model (SDEM) quantified the direction and magnitude of the factors to LE. The SDEM contains a spatial error term and jointly estimates both local and neighborhood associations. This methodology controls for non-independence between census tracts to provide unbiased statistical estimates.ResultsFactors significantly related to an increase in LE, include percentage (%) of the population who identify as Hispanic (beta coefficient [β]: 0.06, p-value [P] < 0.001) and % of age dependent populations (% population < 5 years old and % population > 65) (β: 0.13, P < 0.001). Conversely, the following factors exhibited significant negative LE associations, % of households with no automobile (β: -0.05, P < 0.001), % of mobile homes (β: -0.02, P < 0.001), and % of female headed households (β: -0.11, P < 0.001).ConclusionsResults from the SDEM demonstrate social vulnerability indicators account for additional geographic LE variability beyond commonly studied SDOH. Empirical findings from this analysis can help local health departments identify drivers of spatial health disparities at the local level.

Inefficiencies in a healthcare system with a regulatory split of power: a spatial panel data analysis of avoidable hospitalisations in Austria

Despite generous universal social health insurance with little formal restrictions of outpatient utilisation, Austria exhibits high rates of avoidable hospitalisations, which indicate the inefficient provision of primary healthcare and might be a consequence of the strict regulatory split between the Austrian inpatient and outpatient sector. This paper exploits the considerable regional variations in acute and chronic avoidable hospitalisations in Austria to investigate whether those inefficiencies in primary care are rather related to regional healthcare supply or to population characteristics. To explicitly account for inter-regional dependencies, spatial panel data methods are applied to a comprehensive administrative dataset of all hospitalisations from 2008 to 2013 in the 117 Austrian districts. The initial selection of relevant covariates is based on Bayesian model averaging. The results of the analysis show that supply-side variables, such as the number of general practitioners, are significantly associated with decreased chronic and acute avoidable hospitalisations, whereas characteristics of the regional population, such as the share of population with university education or long-term unemployed, are less relevant. Furthermore, the spatial error term indicates that there are significant spatial dependencies between unobserved characteristics, such as practice style or patients’ utilization behaviour. Not accounting for those would result in omitted variable bias.

Alleviating Spatial Confounding for Areal Data Problems by Displacing the Geographical Centroids

Spatial confounding between the spatial random effects and fixed effects covariates has been recently discovered and showed that it may bring misleading interpretation to the model results. Techniques to alleviate this problem are based on decomposing the spatial random effect and fitting a restricted spatial regression. In this paper, we propose a different approach: a transformation of the geographic space to ensure that the unobserved spatial random effect added to the regression is orthogonal to the fixed effects covariates. Our approach, named SPOCK, has the additional benefit of providing a fast and simple computational method to estimate the parameters. Also, it does not constrain the distribution class assumed for the spatial error term. A simulation study and real data analyses are presented to better understand the advantages of the new method in comparison with the existing ones.

Spatial autoregressive with a spatial autoregressive error term model and its parameter estimation with two-stage generalized spatial least square procedure

Spatial relationship models often use dependence relationships into covariance structures through the autoregressive model. The autoregressive process is shown through the dependence relationship between a set of observations or a location from now on called the dependent spatial model. The Spatial dependent model is divided into two categories: spatial lag and spatial error. The spatial lag regression model is a model that considers dependent variables on an area with other areas associated with it, and the spatial error regression model is a model that takes into account the dependency of error values of an area with errors in other areas associated with it. Models with both dependencies are expressed as spatial autoregressive models with a spatial autoregressive error term (SAR-SAR). These dependencies resulted in the estimation of parameters by the ordinary least square method (OLS) resulting in inconsistent estimators. Therefore a special estimation method is required which results in a consistent estimate of the generalized spatial two-stage least square (GS2SLS). In this paper, we review the parameter estimation of SAR-SAR model with GS2SLS. To complete this paper, we also applicate of SAR-SAR model in dengue hemorrhagic fever (DHF) case in Surakarta, Central Java.

Using independent component analysis to monitor2‐Dgeometric specifications

AbstractFunctional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.

Correlates of range size variation in the Australian seed‐plant flora

AbstractAimTo map and analyse range size variation in the terrestrial seed‐plant flora of Australia in relation to latitude, habitat availability, climate and soils, and to compare mean range size between biomes and growth forms.LocationAustralia.MethodsRange sizes were estimated from herbarium records using alpha‐hulls for 19,227 species and mapped into a set of 0.5° × 0.5° grid cells across Australia. Ordinary‐least squares regressions were used to test for relationships between mean range size, latitude and habitat availability. Simultaneous autoregressive models (SAR) with spatial error terms were used in a multi‐model framework to assess the role of aridity, mean annual temperature (MAT), soil pH, depth and total P concentration in shaping range size variation. Species‐level differences between growth forms (graminoids, herbs, trees, shrubs, climbers) and biomes were assessed using one‐way analysis of variance (ANOVA).Results68% of Australian seed‐plant species have ranges which cover &lt; 1% of the continent. Generally, large ranges are characteristic of graminoids and herbs and are associated with arid and grassland biomes. The smallest ranges were found in Mediterranean ecosystems in the SW corner of the continent, and were typically shrub species. Range size peaked at mid‐latitudes and was not consistently smaller at lower latitudes (contrary to Rapoport's Rule). Increasing aridity, MAT and soil pH were strong predictors of large range size; however, soil depth and P content had little influence in SAR models.Main conclusionsAridity and temperature are the primary drivers of range size variation in the Australian flora. Trait syndromes which promote colonization and survival in arid and grassland habitats (e.g. C4 photosynthesis, wind pollination) have allowed grasses and herbs to occupy large areas of the continent. Ranges were not smaller, on average, in the tropics due to the concentration of large‐ranged species in the widespread arid biome in the centre of the continent.

Effects of construction activities on residential electricity consumption: Evidence from Singapore's public housing estates

This study aims to empirically test the effects of negative environmental externalities (i.e. noise pollution) due to construction activities within half to one kilometer (km) radius and how households react to such externalities by increasing the use of air-conditioners to mitigate noise from the construction work. We use a unique dataset of electricity consumption by public housing residents in Singapore measured at the building level and merge it with the dataset of construction sites for the periods from 2009 to 2011. Using a difference-in-differences approach, we find that electricity consumption by the households living close to the construction sites increases by 6% compared to the households who are not affected by noises from construction sites during the construction periods, after controlling for building and month of the year fixed effects. The results remain robust after controlling for spatial autocorrelated lag and error terms. The economic cost of the construction externalities for each household amounts to approximately S$98 per annum. We also find that the increases in electricity consumption of the affected households were persistent, and the electricity consumption of the affected households did not revert to the pre-construction levels, after the removal of the negative externality.

The spatial configuration of urban crime environments and statistical modeling

The aim of this paper is to discuss the representation of space in statistical models of urban crime. We argue that some important information represented by the properties of space is either lost or hardly interpretable if those properties are not explicitly introduced in the model as regressors. We illustrate the issue commenting on the shortcomings of the two standard approaches to modeling the dispersion of crime in a city: using local attributes of places as regressors, and defining a catch-all spatial component to neutralize the effect of latent spatial factors from the model. As an alternative to the current methods, the metrics of spatial configuration, including those devised by the technique called Space Syntax Analysis, provide useful variables that can be introduced as regressors. Such regressors offer interpretable information on space, behavior, and their interactions, that would otherwise be lost. We therefore consider a set of three configurational variables that represent different forms of centrality and that are thought to have influence on a wide range of human activities. We propose an innovative procedure to adapt these variables to most urban graphs and then, using data from a large area in the city of Genoa (Italy), we show that the three variables are well defined, consistent, noncollinear indicators, with evident spatial meanings. Then we build two sets of Hierarchical Bayesian count models of different urban crime types (“property crime” and “arson and criminal damage”) around some known covariates of crime and we show that the overall quality of the models is improved (with the size of improvement depending on the type of crime) when the three configurational variables are included. Furthermore, we show that what the three variables explain of the overall variability of crime is a sizeable part of what would be the spatial error term of a traditional spatial model of urban crime. While the configurational variables alone cannot provide a goodness of fit as high as the one obtained with a generic spatial term, they have a relevant role for the interpretation of the results, which is ultimately the objective of urban crime modeling.

Spatial clustering of toxic trace elements in adolescents around the Torreón, Mexico lead–zinc smelter

High blood lead (BPb) levels in children and elevated soil and dust arsenic, cadmium, and lead were previously found in Torreón, northern Mexico, host to the world's fourth largest lead-zinc metal smelter. The objectives of this study were to determine spatial distributions of adolescents with higher BPb and creatinine-corrected urine total arsenic, cadmium, molybdenum, thallium, and uranium around the smelter. Cross-sectional study of 512 male and female subjects 12-15 years of age was conducted. We measured BPb by graphite furnace atomic absorption spectrometry and urine trace elements by inductively coupled plasma-mass spectrometry, with dynamic reaction cell mode for arsenic. We constructed multiple regression models including sociodemographic variables and adjusted for subject residence spatial correlation with spatial lag or error terms. We applied local indicators of spatial association statistics to model residuals to identify hot spots of significant spatial clusters of subjects with higher trace elements. We found spatial clusters of subjects with elevated BPb (range 3.6-14.7 μg/dl) and urine cadmium (0.18-1.14 μg/g creatinine) adjacent to and downwind of the smelter and elevated urine thallium (0.28-0.93 μg/g creatinine) and uranium (0.07-0.13 μg/g creatinine) near ore transport routes, former waste, and industrial discharge sites. The conclusion derived from this study was that spatial clustering of adolescents with high BPb and urine cadmium adjacent to and downwind of the smelter and residual waste pile, areas identified over a decade ago with high lead and cadmium in soil and dust, suggests that past and/or present plant operations continue to present health risks to children in those neighborhoods.

Statistische Methoden der kleinräumigen Versorgungsforschung

Accurate modeling of spatial dependencies between observations is a significant challenge in research on regional health-care services. This article provides insight into current methods of modeling relationships in regional health-care service research, with consideration of spatial dependencies. Spatial dependencies may be triggered by spillover effects between neighboring regions and spatially distributed differences in - e.g., morbidity - which are not observable. If not considered in the model, the results of the analyses may be biased. Spatial dependencies can be added to the regression model as a spatial lag or a spatial error term. Using an example study, we illustrate that failing to consider spatial autocorrelation may lead to biased coefficients and/or standard errors. Research on regional health-care services should, therefore, if possible, test for spatial autocorrelation in the data and adjust the model accordingly.

Effects of Construction Activities on Residential Electricity Consumption: Evidence from Singapore's Public Housing Estates

This study aims to empirically test the effects of negative environmental externalities (i.e. noise pollution) due to construction activities within half to one kilometer (km) radius and how households react to such externalities by increasing the use of air-conditioners to mitigate noise from the construction work. We use a unique dataset of electricity consumption by public housing residents in Singapore measured at the building level and merge it with the dataset of construction sites for the periods from 2009 to 2011. Using a difference-in-differences approach, we find that electricity consumption by the households living close to the construction sites increases by 6% compared to the households who are not affected by noises from construction sites during the construction periods, after controlling for building and month of the year fixed effects. The results remain robust after controlling for spatial autocorrelated lag and error terms. The economic cost of the construction externalities for each household amounts to approximately S$98 per annum. We also find that the increases in electricity consumption of the affected households were persistent, and the electricity consumption of the affected households did not revert to the pre-construction levels, after the removal of the negative externality.

The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term

This paper considers the estimation of a linear regression involving the spatial autoregressive (SAR) error term which is nearly nonstationary. The asymptotics properties of the ordinary least squares (OLS), true generalized least squares (GLS) and feasible generalized least squares (FGLS) estimators as well as the corresponding Wald test statistics are derived. Monte Carlo results are conducted to study the sampling behavior of the proposed estimators and test statistics. RÉSUMÉ la présente communication se penche sur l'estimation d'une régression linéaire, comportant l'erreur autorégressive spatiale (SAR) qui est quasiment non stationnaire. Les propriétés asymptotiques des estimateurs aux moindres carrés ordinaires, des moindres carrés généralisés et des moindres carrés réalisables et généralisés, ainsi que les statistiques d'essai de Wald, sont dérivés. On calcule les résultats de Monte Carlo afin d’étudier le comportement d’échantillonnage des estimateurs proposés et des statistiques d'essai. EXTRACTO Este estudio considera la estimación de una regresión lineal donde se incluye el término de error autorregresivo espacial (SAR) que es casi no estacionario. Se derivan las propiedades asimptóticas de los estimadores de mínimos cuadrados ordinarios (MCO), mínimos cuadrados generalizados (MCG) verdaderos y mínimos cuadrados generalizados factibles (MCGF), así como las estadísticas correspondientes de la prueba Wald. Los resultados de Monte Carlo se llevan a cabo para estudiar el comportamiento de muestreo de los estimadores y las estadísticas de pruebas propuestos. 摘要: 本文使用线性回归方法对近似非平稳的空间自回归 (SAR) 误差项进行估计,进而得到了普通最小二乘法 (OLS) 、真广义最小二乘法 (GLS) 、可行的广义最小二乘法 (FGLS) 三种估计器的渐近特性以及相应的 Wald 检验统计量。通过蒙特卡洛仿真结果研究了这几种估计器和检验统计量的采样行为。